I see you've uploaded an image. I'll analyze the content of the image to extract and solve the mathematical problem depicted.

Let's begin.The image contains a mathematical equation:

$\frac{dy}{dx} = e^{x-y}$

This is a separable differential equation, which means we can rearrange it to separate variables $x$ and $y$. Here's how to solve it step-by-step:

Step 1: Rewrite the equation to separate variables

We want all the $y$-related terms on one side and the $x$-related terms on the other side. Start by rewriting the equation:

$\frac{dy}{dx} = e^{x-y} = e^x e^{-y}$

Now, separate the variables:

$e^y \, dy = e^x \, dx$

Step 2: Integrate both sides

Integrate both sides of the equation:

$\int e^y \, dy = \int e^x \, dx$

On the left-hand side, the integral of $e^y$ is $e^y$, and on the right-hand side, the integral of $e^x$ is $e^x$:

$e^y = e^x + C$

where $C$ is the constant of integration.

Step 3: Solve for $y$

Now, take the natural logarithm of both sides to solve for $y$:

$y = \ln(e^x + C)$

Thus, the solution to the differential equation is:

$y = \ln(e^x + C)$

This is the general solution to the given differential equation.

Do you need further details or clarification? Here are some additional questions to explore:

1. What happens to the solution when $C = 0$?
2. How can we check the solution by differentiating it?
3. What is the particular solution if an initial condition is given, such as $y(0) = 1$?
4. What would the graph of $y = \ln(e^x + C)$ look like?
5. How can we interpret this solution in terms of exponential growth or decay?

Tip: When solving separable differential equations, always make sure to check whether the variables can be separated before starting the integration process.